0,2

Column 0 is A006690.

Matrix diagonalization method: define triangular matrix P by P(n, k) = ((n+1)^3)^(n-k)/(n-k)!, n>=k>=0 and diagonal matrix D(n, n) = n+1, then T is given by T = P^-1*D^3*P.

Triangle begins:

1;

56,8;

7965,513,27;

2128064,81856,2368,64;

914929500,23846125,469625,7625,125;

576689214816,10943504136,160767720,1898856,19656,216; ...

which equals the matrix cube of triangle A107671:

1;

8,2;

513,27,3;

81856,2368,64,4;

23846125,469625,7625,125,5;

10943504136,160767720,1898856,19656,216,6; ...

(PARI) {T(n, k)=local(P=matrix(n+1, n+1, r, c, if(r>=c, (r^3)^(r-c)/(r-c)!)), D=matrix(n+1, n+1, r, c, if(r==c, r))); if(n>=k, (P^-1*D^3*P)[n+1, k+1])}

Cf. A107667, A107671, A107674, A006690.

Sequence in context: A093255 A115410 A036197 this_sequence A005932 A109737 A092077

Adjacent sequences: A107673 A107674 A107675 this_sequence A107677 A107678 A107679

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Jun 07 2005